Lehman a 'kindergarten show' next to any default

"There is virtually no chance that we'll have any kind of default... the markets understand that the debt ceiling is not going to be catastrophic," says Bill Miller, Legg Mason Opportunity Trust Fund manager, discussing how the government shutdown will likely impact the markets.

Stock market traders and investors don't believe the fight over the debt ceiling will result in a U.S. default, closely followed value investor Bill Miller told CNBC on Tuesday, hours after the first government shutdown in 17 years.

But if for some reason the federal government didn't pay the interest on the debt, he warned, that "would make Lehman Brothers look like a kindergarten show."

"The real issue is the debt ceiling, not the government shutdown," Miller said in a "Squawk Box" interview. The Treasury has set Oct. 17 as the deadline for the nation's borrowing authority to be increased.

Miller—portfolio manager of the Legg Mason Opportunity Trust fund—pointed out that the debt ceiling fight in the summer of 2011 resulted in a downgrade of the U.S. by Standard & Poor's. "But that was in conjunction with the European crisis. So we don't have that European crisis now, and there's virtually no chance we'll have any kind of default."